Consumers suffer from important information asymmetries with respect to safety quality, being the case that when a passenger boards a plane she does not know whether she is choosing a safe or risky airline. However, service quality is more directly perceived by passengers. In this paper, we apply data envelopment analysis (DEA) methodology to synthesise some partial indicators of safety and service quality. We measure these quality variables by using 11 complementary indicators: three corresponding to the safety dimension and eight to the service dimension. The relative performance of each airline is discussed according to the results of these partial indicators, and DEA methodology is used to obtain a better understanding of the overall picture of safety and service quality. As consumers are usually better informed about the service quality of airlines, we will study the interrelationship between these two sides of global quality, trying to anticipate if some of the misinformation regarding air transport safety could be reduced.